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Linear Motion: calculating height of cliff given speed of sound and time

  1. Feb 24, 2012 #1
    1. The problem statement, all variables and given/known data
    A student standing on top of a cliff drops a rock down below into the water and hears it splash 3 seconds later. The speed of sound is 330m/s, what is the height of the cliff


    2. Relevant equations
    v= d/t
    v2 = v1 + at
    d = v2-1/2 at2
    d = (v1 + v2)t
    v2 squared = v1 squared + 2ad
    d = v1t + at2


    3. The attempt at a solution
    when I first saw this, I thought of echos
    v=d/t
    330 = d/3
    d=990
    and then divide by two since echo
    d= 990/2
    d= 495
    however, that is horizontal distance not vertical, so I listed my knowns but am unsure as what to do with the 330 m/s

    knowns for rock
    v1= 0 (since he dropped the rock)
    v2=
    a = -9.8 m/s2
    t = 3s
    d =

    knowns for speed of sounds
    v= 330 m/s
    t = 3s
    d= ?

    then setting the distance of both of these equal to each other and solving for d?
     
  2. jcsd
  3. Feb 24, 2012 #2

    PeterO

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    Homework Helper

    Some of the time [most?] is taken up with the rock falling. A small amount at the end is the sound travelling up at 330 m/s.

    For example, if you drop something and it falls for 3 seconds, it falls a little less than 45m

    At 330 m/s, the sound would take about 0.15 seconds to come back the 45 m

    We thus know the cliff is less than 45 m high.
     
  4. Feb 25, 2012 #3
    hmm, so if I change my variables in the "knowns for rock"
    v1: 0
    v2:
    a: -9.8m/s
    t: t-3
    d:

    and sub in to solve for d...

    d rock = v1t + 0.5at squared
    = (0)t + 0.5(-9.8)(t-3) squared
    = -4.9tsquared + 29.4t -44.1

    dsound =vt
    = (330)t

    330t = -4.9squared + 29.4t -44.1
    = -4.9squared -300.6t - 44.1
    = [-b +/- √(b squared-4ac)]2a
    = [300.6 +/- √(89496)]-9.8
    t= -61.2 or -.15
    I get the same 0.15 time however, mine is negative for some reason..
     
  5. Feb 25, 2012 #4

    PeterO

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    Homework Helper

    I think that first time should be 3-t

    That change of sign may fix things
     
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